0/1背包问题

 1 #include <iostream>
 2 #include <vector>
 3 using namespace std;
 4 const int MIN=0x80000000;
 5 const int N=3;   //物品数量
 6 const int V=5;  //背包容量
 7 int f[N+1][V+1];
 8 
 9 int Package(int *W,int *C,int N,int V);
10 void main(int argc,char *argv[])
11 {
12  int W[4]={0,7,5,8};      //物品权重
13  int C[4]={0,2,3,4};      //物品大小
14  int result=Package(W,C,N,V);
15  if(result>0)
16  {
17   cout<<endl;
18   cout<<"the opt value:"<<result<<endl;
19   int i=N,j=V;
20   while(i)
21   {
22    if(f[i][j]==(f[i-1][j-C[i]]+W[i]))
23    {
24     cout<<i<<":"<<"w="<<W[i]<<",c="<<C[i]<<endl;
25     j-=C[i];
26    }
27    i--;
28   }
29  }
30  else
31   cout<<"can not find the opt value"<<endl;
32  return;
33 }
34 
35 int Package(int *W,int *C,int N,int V)
36 {
37  int i,j;
38  memset(f,0,sizeof(f));  //初始化为0
39 
40  for(i=0;i<=N;i++)
41  for(j=1;j<=V;j++)               //此步骤是解决是否恰好满足背包容量，
42   f[i][j]=MIN;                //若“恰好”满足背包容量，即正好装满背包，则加上此步骤，若不需要“恰好”，则初始化为0
43     
44  for(i=1;i<=N;i++)
45   for(j=C[i];j<=V;j++)
46   {
47    f[i][j]=(f[i-1][j]>f[i-1][j-C[i]]+W[i])?f[i-1][j]:(f[i-1][j-C[i]]+W[i]);
48    cout<<"f["<<i<<"]["<<j<<"]="<<f[i][j]<<endl;
49   }
50  return f[N][V];
51 }

 1 代码2
 2 
 3 #include <iostream>
 4 #include <vector>
 5 using namespace std;
 6 const int MIN=0x80000000;
 7 const int N=3;   //物品数量
 8 const int V=5;  //背包容量
 9 int f[V+1];
10 
11 int Package(int *W,int *C,int N,int V);
12 void main(int argc,char *argv[])
13 {
14  int W[4]={0,7,5,8};      //物品权重
15  int C[4]={0,2,3,4};      //物品大小
16  int result=Package(W,C,N,V);
17  if(result>0)
18  {
19   cout<<endl;
20   cout<<"the opt value:"<<result<<endl;
21  }
22  else
23   cout<<"can not find the opt value"<<endl;
24  return;
25 }
26 
27 int Package(int *W,int *C,int N,int V)
28 {
29  int i,j;
30  memset(f,0,sizeof(f));  //初始化为0
31 
32  for(i=1;i<=V;i++)               //此步骤是解决是否恰好满足背包容量，
33   f[i]=MIN;                //若“恰好”满足背包容量，即正好装满背包，则加上此步骤，若不需要“恰好”，则初始化为0
34     
35  for(i=1;i<=N;i++)
36   for(j=V;j>=C[i];j--)    //注意此处与解法一是顺序不同的，弄清原因
37   {
38    f[j]=(f[j]>f[j-C[i]]+W[i])?f[j]:(f[j-C[i]]+W[i]);
39    cout<<"f["<<i<<"]["<<j<<"]="<<f[j]<<endl;
40   }
41  return f[V];
42 }